If x is an integer, is x|x| < 2^x ?
1) x<0
2) x=-10
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Is x|x| < 2^x?
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Patrick_GMATFix
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|x| = x when x is positive, but -x when x is negative. So we can think of this as a set of two questions:
If x>0, is x^2 < 2^x?
If x<0, is -x^2 < 2^x?
The full solution below shows how to solve in under a minute. It is taken from the GMATFix App.
-Patrick
If x>0, is x^2 < 2^x?
If x<0, is -x^2 < 2^x?
The full solution below shows how to solve in under a minute. It is taken from the GMATFix App.
-Patrick
- Check out my site: GMATFix.com
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Hi GmatGreen,
This DS question is built around a few Number Properties. Whether you know the Number Properties already or not, you CAN figure then out as you work through the question. We're told that X is an integer. We're asked "is X|X| < 2^X?" This is a YES/NO question.
Fact 1: X < 0
This means that X is NEGATIVE. Plugging any negative value into the given question, we'd have:
X|X| vs. 2^X
Neg|Neg| vs. 2^Neg
Neg(Pos) vs. Pos
Neg. vs. Pos
So X|X| will always be negative and 2^X will always be positive. This means that the answer to the question will ALWAYS be YES.
Fact 1 is SUFFICIENT
Fact 2: X = -10
With this one value, we COULD plug in -10 to the given question and then answer it. There would be just one answer.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This DS question is built around a few Number Properties. Whether you know the Number Properties already or not, you CAN figure then out as you work through the question. We're told that X is an integer. We're asked "is X|X| < 2^X?" This is a YES/NO question.
Fact 1: X < 0
This means that X is NEGATIVE. Plugging any negative value into the given question, we'd have:
X|X| vs. 2^X
Neg|Neg| vs. 2^Neg
Neg(Pos) vs. Pos
Neg. vs. Pos
So X|X| will always be negative and 2^X will always be positive. This means that the answer to the question will ALWAYS be YES.
Fact 1 is SUFFICIENT
Fact 2: X = -10
With this one value, we COULD plug in -10 to the given question and then answer it. There would be just one answer.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
